code: def convolution2d_backward_as_a_convolution(
      layer: nn.Conv2d,
      activations: List[torch.Tensor],
      backprops: torch.Tensor,
  ) -> Dict[nn.Parameter, torch.Tensor]:
      """
      Computes per sample gradients for Conv2d layers using backward.
      This is an alternative implementation and is not used because it is slower in many contexts.
  
      Args:
          layer: Layer
          activations: Activations
          backprops: Backpropagations
      """
      activations = activations[0]
      batch_size = activations.shape[0]
      input_size = activations.shape[1]
      output_size = backprops.shape[1]
  
      # activations has shape (B, I, H, W)
      # backprops has shape (B, O, H, W)
      activations_ = activations.view(
          batch_size,
          layer.groups,
          input_size // layer.groups,
          activations.shape[2],
          activations.shape[3],
      )  # (B, G, I/G, H, W)
  
      activations_ = activations_.view(
          activations_.shape[0] * activations_.shape[1],
          activations_.shape[2],
          activations_.shape[3],
          activations_.shape[4],
      )  # (B*G, I / G, H, W)
      activations_ = activations_.transpose(
          0, 1
      )  # (I / G, B * G, H, W)
      backprops_ = backprops.view(
          backprops.shape[0] * backprops.shape[1],
          1,
          backprops.shape[2],
          backprops.shape[3],
      )  # (B*O, 1, H, W)
  
      # Without groups (I, B, H, W) X (B*O, 1, H, W) -> (I, B*O, H, W)
      # With groups (I / G, B*G, H, W) X (B*O, 1, H, W) -> (I / G, B * O, H, W)
      weight_grad_sample = F.conv2d(
          activations_,
          backprops_,
          bias=None,
          dilation=layer.stride,
          padding=layer.padding,
          stride=layer.dilation,
          groups=batch_size * layer.groups,
      )
      weight_grad_sample = weight_grad_sample.view(
          input_size // layer.groups,
          batch_size,
          output_size,
          *weight_grad_sample.shape[-2:],
      )  # (I / G, B, O, H, W)
      weight_grad_sample = weight_grad_sample.movedim(
          0, 2
      )  # (B, O, I/G, H, W)
      weight_grad_sample = weight_grad_sample[
          :, :, :, : layer.weight.shape[2], : layer.weight.shape[3]
      ]
  
      ret = {layer.weight: weight_grad_sample}
      if layer.bias is not None:
          ret[layer.bias] = torch.sum(backprops, dim=[-1, -2])
  
      return ret
  
file_path: opacus/opacus/grad_sample/conv.py
imports: import math
  from typing import Dict, List, Union
  import numpy
  import torch
  import torch.nn
  import torch.nn.functional
  from opacus.utils.tensor_utils import unfold2d, unfold3d
  from opt_einsum import contract
  from .utils import register_grad_sampler
label_desc: Use image node_id 2 for calling a global function with example usage: convolution2d_backward_as_a_convolution(layer, activations, backprops) and returns: ret